From Nothingness to EAS Scalar-Field Ontology

Abstract

Entanglement-Algebraic Spacetime (EAS) is developed from a foundational physical stance in which no primitive spacetime, geometry, matter, field medium, or other physical background is assumed. The EAS scalar-field (SF) construction introduced here is therefore not itself a primordial physical substrate. It is a formal mathematical apparatus used to state the minimal objects, relations, ordering, and admissibility conditions from which later report structures and physical interfaces may be constructed. This paper fixes that formal ontology and the vocabulary required to keep those levels distinct. An admitted ordered SF family is defined on one common nonempty formal point set. Every point has exactly three ordered association slots; each slot is either defined or undefined, and every certified target is non-self, pairwise distinct at its point, and fixed after definition. A single global rank–3 presentation cycle selects the active slot. The sole primitive relational commitment is universal association reachability: every point is reachable from every other point by a finite succession of associations, whether or not a concrete succession has been explicitly recorded. Relational paths are not additional ontological objects. They are modeling abstractions defined from minimum association-connection point count. Consequently, different minimum realizations with the same endpoints and the same minimum count cannot be distinguished as different relational paths. More strongly, no admissible later operation can split such an indistinguishability class by acting on one purported path and not another; such an operation would presuppose the very distinction it attempts to create. Native second-order ordering is retained only at the foundational level required here: each completed realization is a deterministic bijection of the immutable formal point set whose nontrivial elementary actions are exact scalar-value transpositions. Detailed phase-specific recurrence theory is assigned to a separate paper. SF sectors, exterior complements, and admitted bounded-support records are defined without importing geometric enclosure or ambient space. The paper concludes with a strict ontology–report–interface firewall and identifies two remaining native adjudications: the universal rule for defining a previously undefined association target and the universal admission/classification rule for bounded-support records. The paper does not claim to prove why physical reality emerges from nothingness; it specifies the formal ontology under which such later questions may be posed without silently presupposing the structures to be explained.